In a statement, Williams said the proposal "significantly undervalues Williams."

Williams further announced that it has retained Barclays and Lazard to help it review "strategic alternatives, which could include, among other things, a merger, a sale of Williams, or continuing to pursue the company's existing operating and growth plan."

However, some traders aren't too optimistic that further upside is ahead for the stock, which closed Monday at $65.06.

"It seems clear that Energy Transfer Equity came in with a pretty nice bid for WMB," David Seaburg, head of equity sales trading at Cowen, wrote to CNBC. "Maybe they bump it up some, but not much more. And I don't think another buyer emerges."

"Of course the upside is in play, but technically, from a trading point of view, this is a very difficult story to trade, just because of the massive size of this gap," he said Monday on CNBC's "Trading Nation."

Analysts, meanwhile, are sure to closely watch the company's next moves.

In a note titled "Who's Your Daddy This Time?" following the Father's Day announcement, Jefferies analyst Christopher Sighinolfi wrote that he is awaiting "more information with respect to the timetable set for Williams to conclude its exploration of strategic alternatives."

Want to be part of the Trading Nation? If you'd like to call in to our live Monday show, email your name, number and question to TradingNation@cnbc.com.